I do not press my binding strip in half.
I baste the raw edges together, instead.
The reason I do not press my binding strip in half is that when the binding makes its turns around the edge of the quilt, the "center crease" is moved over two or three threads and then does not turn as nicely as it could.
Think of turning a corner with a car or concentric arcs. The inside corner does not cover as much ground as the outside corner.